Physics in the Laundromat

Many of us have had the opportunity to observe clothes tumbling in a dryer at a laundromat, and perhaps have reflected how the angular velocity of the drum must be less than √ g/r, where r is the radius of the drum and g is the accelerator due to gravity, if the clothes are to fall free of the drum and make improved contact with the hot air. Another common observation is the vibration of a washing machine during the start of its spin cycle. Indeed, if the load is poorly distributed the vibration becomes so violent that the washer cannot spin up until the load is redistributed. If one defeats the interlock on the door of a top-loading washer during a typical spin cycle the center of the rotor will be observed to move in a small circle, possibly off center, whose radius is a measure of the imbalance of the load. The motion of the axis of the drum of the washer is an example of the motion of unbalanced shafts of large rotating machines, as has been well described by Landau and Kitaigorodsky in a popular book [1]. Here we analyze a simple model of a washer that contains the essential physics. The related topic of whirling of a vertical wire has been treated by Pippard [2].